Four neural layered intelligence architecture for cross ternary nanofluid with waste dispersion over Riga paraboloid under control interactions

Significance: The integration of advanced control mechanisms, waste discharge analysis and innovative supervised neural network methodology with four hidden layers marks a significant step forward in analyzing thermal and mass transport processes in nanofluids. Motive: This study explores the dynamics of nanofluid heat and mass transport by integrating advanced mathematical modeling with neural network methodology over a Riga paraboloid surface. It focuses on active and passive control mechanisms, waste discharge concentration and the infinite shear rate viscosity of the cross-fluid model. Active and passive controls are analyzed to enhance thermal and mass transport efficiency through constant nanoparticle surface concentration and involvement of Brownian motion/thermophoresis, respectively. The process of waste discharge concentration addresses the environmental and operational impacts of nanoparticle dispersions in a nanofluid. Methodology: To predict the solution of this problem, a four-hidden-layer neural network mechanism is employed. This neural network mechanism is trained on the numerical data obtained from a Matlab bvp4c solution over a restricted parameter range and then used to predict the solutions for highly nonlinear boundary value problems over a wider parameter range. Findings: A combination of ANN predictions on the interval [2, 5] based on bvp4c results over the interval [0, 2] was obtained. The gradient, the Mu parameter and validation checks for the fitting mechanism for the ANN scheme gave good results. The Hartmann number and infinite shear parameter were found to contribute to an increase in the velocity magnitude of the ternary fluid.